Ensemble Aggregation Approaches for Functional Optimization

In this work we investigate the use of ensemble methods, consisting in the aggregation of several approximating models, in the context of functional optimization. In fact, while ensemble techniques are routinely employed in the machine learning literature for classification and regression, there is little research on their application to general optimization problems. Here we consider two strategies to aggregate different solutions to a functional optimization problem, based on optimized weighted averaging and aggregation over the minimum, the latter also in approximate version. A theoretical analysis of approximate functional optimization in the context of ensemble aggregation is provided. Then, simulation results are reported to showcase the advantages of ensembles for functional optimization, in terms of better accuracy and improved robustness with respect to single solutions.